Alexander Irvine was educated in Edinburgh, came to Philadelphia in 1727 and was appointed Professor of Mathematics and Surveying at William & Mary in 1727.
From the Executive Journals of the Council of Colonial Virginia, H.R. McIlwaine, Editor. Richmond; Supt. of Public Printing, 1930, page 167, v.4:
"In the Virginia Council on February 27, 1727: This Board having received information that Mr. Allen one of the Surveyors appointed for running the dividing line between this Colony and No. Carolina declines going on that service being hindred(sp) by the dangerous indisposition of his wife, the Governor with the advice of the Council was pleased to nominate and appoint Mr. Alexander Irwin(sp) Professor of the Mathematicks(sp) in the College of William & Mary in the room of the said Mr. Allen, and in case he shall refuse to undertake the same, then Mr. Drury Stith is appointed for that service."
This quotation with no source is included in Professor Irvine's Faculty-Alumni File: "The river Irvine swelled near four feet from rain and put the mathematics professor into the vapours. The river Irvine christened in honor of our learned professor runs into the Dan 4 miles to south of the line"
Professor Irvine died in 1732.
According to Google: The Smith River is a river in the state of Virginia and North Carolina. It is a tributary of the Dan River. According to the United States Geological Survey, variant names are Irvin River, Irvine River, and Smiths River.